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The class now supports NonMainThreadScheduler, so its name should also
be changed. File names are also updated.

Bug: 826203
Change-Id: I49c08a359db10d28db5db434b8db5e5b0c985e6f
Reviewed-on: https://chromium-review.googlesource.com/1011862Reviewed-by: Kentaro Hara <haraken@chromium.org>
Reviewed-by: Alexander Timin <altimin@chromium.org>
Commit-Queue: Yuta Kitamura <yutak@chromium.org>
Cr-Commit-Position: refs/heads/master@{#550548}